Elasticity imaging of incompressible biological soft tissue from an incomplete displacement measurement

Abstract

Elasticity imaging has great potential in soft tissue characterization since the tissue elasticity is usually related to some abnormal, pathological process. Internal tissue deformation induced by externally applied mechanical forces has been evaluated to characterize tissue elasticity. For a quantitative elasticity imaging, material parameter such as Young's modulus must be reconstructed from ultrasonic measurement of internal displacement. A method to estimate the elastic modulus of an isotropic, inhomogeneous, incompressible elastic 3-D medium using measured displacement data is formulated by inversely solving the forward problem for static deformation. A finite-element based model for static deformation is proposed and then rearranged for solving the distribution of the shear modulus of the soft tissue from a knowledge of the displacement within the tissue. When the force boundary condition is unknown, it reconstructs the relative value of the elastic modulus of the tissue using the displacement data. The feasibility of the proposed method is demonstrated using the simulated deformation data of the simple three-dimensional inclusion problem. The performance of the algorithm with noise in the diplacement measurement data is teseted using numerical simulations. The results show that the relative shear modulus may be reconstructed from the displacement data measured locally in the region of interest within an isotropic, incompressible medium, and that the relative shear modulus can be recovered to some degree of accuracy from only one-dimensional displacement data. Details of how to apply this method under clinical conditions is also discussed.